Cluster Before You Hallucinate: Approximating Node-Capacitated Network Design and Energy Efficient Routing
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arXiv
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| Format: | Preprint |
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2014
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| _version_ | 1866910359093248000 |
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| author | Krishnaswamy, Ravishankar Nagarajan, Viswanath Pruhs, Kirk Stein, Cliff |
| author_facet | Krishnaswamy, Ravishankar Nagarajan, Viswanath Pruhs, Kirk Stein, Cliff |
| contents | We consider the following node-capacitated network design problem. The input is an undirected graph, set of demands, uniform node capacity and arbitrary node costs. The goal is to find a minimum node-cost subgraph that supports all demands concurrently subject to the node capacities. We consider both single and multi-commodity demands, and provide the first poly-logarithmic approximation guarantees. For single-commodity demands (i.e., all request pairs have the same sink node), we obtain an $O(\log^2 n)$ approximation to the cost with an $O(\log^3 n)$ factor violation in node capacities. For multi-commodity demands, we obtain an $O(\log^4 n)$ approximation to the cost with an $O(\log^{10} n)$ factor violation in node capacities. We use a variety of techniques, including single-sink confluent flows, low-load set cover, random sampling and cut-sparsification. We also develop new techniques for clustering multicommodity demands into (nearly) node-disjoint clusters, which may be of independent interest.
Moreover, this network design problem has applications to energy-efficient virtual circuit routing. In this setting, there is a network of routers that are speed scalable, and that may be shutdown when idle. We assume the standard model for power: the power consumed by a router with load (speed) $s$ is $σ+ s^α$ where $σ$ is the static power and the exponent $α> 1$. We obtain the first poly-logarithmic approximation algorithms for this problem when speed-scaling occurs on nodes of a network. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1403_6207 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Cluster Before You Hallucinate: Approximating Node-Capacitated Network Design and Energy Efficient Routing Krishnaswamy, Ravishankar Nagarajan, Viswanath Pruhs, Kirk Stein, Cliff Data Structures and Algorithms 68W25, 05C21, 05C85 F.2.2; G.2.2 We consider the following node-capacitated network design problem. The input is an undirected graph, set of demands, uniform node capacity and arbitrary node costs. The goal is to find a minimum node-cost subgraph that supports all demands concurrently subject to the node capacities. We consider both single and multi-commodity demands, and provide the first poly-logarithmic approximation guarantees. For single-commodity demands (i.e., all request pairs have the same sink node), we obtain an $O(\log^2 n)$ approximation to the cost with an $O(\log^3 n)$ factor violation in node capacities. For multi-commodity demands, we obtain an $O(\log^4 n)$ approximation to the cost with an $O(\log^{10} n)$ factor violation in node capacities. We use a variety of techniques, including single-sink confluent flows, low-load set cover, random sampling and cut-sparsification. We also develop new techniques for clustering multicommodity demands into (nearly) node-disjoint clusters, which may be of independent interest. Moreover, this network design problem has applications to energy-efficient virtual circuit routing. In this setting, there is a network of routers that are speed scalable, and that may be shutdown when idle. We assume the standard model for power: the power consumed by a router with load (speed) $s$ is $σ+ s^α$ where $σ$ is the static power and the exponent $α> 1$. We obtain the first poly-logarithmic approximation algorithms for this problem when speed-scaling occurs on nodes of a network. |
| title | Cluster Before You Hallucinate: Approximating Node-Capacitated Network Design and Energy Efficient Routing |
| topic | Data Structures and Algorithms 68W25, 05C21, 05C85 F.2.2; G.2.2 |
| url | https://arxiv.org/abs/1403.6207 |